The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

Item response theory (IRT) has proven to be a very powerful and useful measurement tool. However, most of the IRT models that have been proposed, and all of the models commonly used, require the assumption of unidimensionality, which prevents their application to a wide range of tests. The few models that have been proposed for use with…

Conventional methods of multivariate normal analysis do not apply when the variables of interest are not observed directly, but must be inferred from fallible or incomplete data. For example, responses to mental test items may depend upon latent aptitude variables, which modeled in turn as functions of demographic effects in the population. A…

Considers a class of estimation procedures for the factor model. The procedures are shown to yield estimates possessing the same asymptotic sampling properties as those from estimation by maximum likelihood or generalized last squares, both special members of the class. General expressions for the derivatives needed for Newton-Raphson…

The robustness of LISREL computer program maximum likelihood estimates under specific conditions of model misspecification and sample size was examined. The population model used in this study contains one exogenous variable; three endogenous variables; and eight indicator variables, two for each latent variable. Conditions of model…

It is shown that the common and unique variance estimates produced by a type of estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. A simple alternative method of specifying the Bayesian parameters required by the procedure is…

A goodness of fit test presented by Andersen (EJ 143 939) is shown to be incorrect. The correct test is described and a re-analysis of Andersen's data is provided. (Author/CTM)

Graham Douglas' claims (TM 503 496) that the X2-test statistics of the paper, "Paired Comparisons with Individual Differences" (EJ 143 939), are incorrect are acknowledged to be justified (Author/CTM)

A multiple time series is defined as the sum of an autoregressive process on a line and independent Gaussian white noise or a hyperplane that goes through the origin and intersects the line at a single point. This process is a multiple autoregressive time series in which the regression matrices satisfy suitable conditions. For a related article…

The properties of nonmetric multidimensional scaling one explored by specifying statistical models, proving statistical consistency, and devloping hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. (Author/LMO)

After introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data, an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed. The possibility of testing various hypotheses is discussed and the algorithm is applied to some existing data…

The author shows that correlation studies can be affected by self-selection bias when questionnaire response is poor, contrary to the common supposition that only loss of degrees of freedom or precision result. Tests are suggested for the ensuing self-selection bias. (Author/LMO)

If the quantitative result of a study is observed only when the mean difference is statistically significant, the observed mean difference, variance, and effect size are biased estimators of corresponding population parameters. The exact distribution of sample effect size and the maximum likelihood estimator of effect size are derived. (Author/BW)

The case of adaptive testing under a multidimensional logistic response model is addressed. An adaptive algorithm is proposed that minimizes the (asymptotic) variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The item selection criterion is a simple expression in closed form. In addition, it is…

Research discussed in this paper was conducted as part of an ongoing large-scale simulation study to evaluate methods of calibrating pretest items for computerized adaptive testing (CAT) pools. The simulation was designed to mimic the operational CAT Armed Services Vocational Aptitude Battery (ASVAB) testing program, in which a single pretest item…